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Chapter 9 Review - Part II

# Chapter 9 Review - Part II - Comparing Two Means Two groups...

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Comparing Two Means Two groups can be compared on a response variable if we compare their . I . Confidence Intervals Let μ 1 : mean corresponding to the response variable for the first group. μ 2 : mean corresponding to the response variable for the second group. We can compare the two groups by constructing a confidence interval of the difference Step I : Assumptions : i) samples from two groups. ii) Approximate population distribution for each of the two groups. Note : This is mainly important for small sample sizes but our confidence interval would still hold if this assumption is violated even for small sample sizes.

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Step II : Let us draw samples of sizes n 1 and n 2 from the two groups. Let the sample means for the two groups be and respectively (Here x-bar = ) Thus, the difference in sample means will be . Step III : As for the single mean, the confidence interval for is obtained by adding and subtracting a to its point estimate As before, the margin of error is the product of the appropriate and the of . It can be shown that the standard error of is given by s.e = where and are the of the first and second samples. Note : Always remember that for estimates calculated from samples, s.e (est 1 – est 2) =
1 -bar and est 2 is x 2 -bar, s.e (est 1) is S 1 2 /n 1 while s.e (est 2) is S 2 2 /n 2. So, for the difference of means, the margin of error will be m.e = The exact degrees of freedom of the t score is difficult to calculate*. Any statistical software will give you the value. But, if and , the df becomes . Otherwise, the degrees of freedom can be taken to be the smaller of . If we need a 95% (99%) confidence interval, t = t 0.025 (t 0.005 ) which is the t score with right tail area/probability 0.025 (0.005).

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Chapter 9 Review - Part II - Comparing Two Means Two groups...

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